4.3.2 - Hyper-E Numbers

As a kid, I didn't actually
come up with any names for large numbers, save the erroneous
centillionillion ( now called ecetonplex. See #425), using my notations. I was primarily on a quest to
reach infinity, so any finite number, no matter how large, could never
be more than a way station. However, since coming up with names is kind
of part of the Large Number tradition, I'll indulge "a bit", and by a
bit I mean quiteA LOT :)

When forming number
examples in my treatise on large numbers, I had a tendency to use the
centillion as a base. This preference was due partly because it was my
favorite number, and partly to avenge the centillion after being trumped
by the googolgong. Seeing how I've kind of appropriated the googolgong
as my own, I now find it fitting to use it, along with the googol as a
base.

Following Jonathan Bowers' tradition, I'll divide my number names into "Regiments" (analogous to Bowers' "Groups") to make it easier to keep track. A regiment is simply a collection of googolism's which are of similar order-type, construction, and size. Regiments may be further sub-divided into Squads, which can be further sub-divided into Series. Members of a regiment (called recruits) are numbered, giving them an official order within the regiment, as well as in the entire system. For the purposes of this list a googolismis a specific name given to a specifically defined number. In some cases the same number may be given more than one name, in which case each name is a unique googolism. Googolism's will always be written in italics. The list enumerates the number of unique googolism'scurrently recognized as part of the ExE system. It therefore doesn't include names in ExE which have become defunct. The number of distinct numbers given a name is another closely related enumeration. In general the number of numbers named and the number of number names should not differ significantly since most numbers are only given one name, and no number has more than a few names.

In this article I introduce the E# numbers. These are broken into a total of 10 regiments, each one corresponding to a major milestone googolism: guppy, grangol, greagol, gigangol, gorgegol, gulgol, gaspgol, ginorgol, gargantuul, and googondol. In total there are 1141 googolism's introduced in this article! In the next article we continue with the xE# numbers.

Better get started, we have a loooooooooong way to go! Let's begin...

Guppy

Regiment

Category 1

Members: 504

(1 - 504)

First comes the Guppy Regiment, the smallest regiment in the system.

Before we begin let me note that a googol = 10^100 and a googolplex = 10^10^100. This forms the basis of this regiment, although neither the googol, googolplex, nor any other members of the so called Googol Series are official members of this regiment, since I did not coin any of these. The googol and googolplex were coined by Edward Kasner and his nephew Milton Sirotta. Further members such as googolduplex, googoltriplex, etc. have gained popularity and acceptance in the googology community and quite a few of these were used by Jonathan Bowers' himself. I can not claim to have come up with any of these. The following googolism's however, were coined by me.

We will begin with a number which is microscopic ... by googological standards, but is still decently large in most ordinary situations...

(1)eyelash mite = 2E4 = 2*(10^4) = 20,000

A "eyelash mite" is a very very tiny create that is said to live on human eyelashes. It can measure as little as 0.25 mm across. By googological standards 20,000 is exceptionally tiny, but it's just large enough that in most situations people would agree it's still a "large" number. 20,000 seconds would be 5.5 hours. 20,000 minutes would be 13.8 days. 20,000 hours would be 2.28 years, and 20,000 days would be 54.75 years. It would take 6 days and 22 hours to waste 20,000 gallons of water with a facet on at full force (typical rate is 2.0gal/min). If this water were turned into a uniform sphere it would have a diameter of 5.25 meters. Since the average human height is 1.78 meters, this sphere would stand 2.95 times taller than an the average person! Sounds pretty big now! This is only the beginning. Next up is the slightly larger (by a factor of 2.5) ...

(2)dust mite = 5E4 = 5*(10^4) = 50,000

A "dust mite" is a very tiny creature, only a fraction of a millimeter in length ( typical figure given is 0.35 mm), so small that it is barely visible with the unaided eye! By way of metaphor, a dust mite is a number so small in googology that it exists below the astronomical threshold and is therefore "microscopic"( I typically count a million as the bare minimum to be classified as "astronomical". Luis Epstein describes a million as the "smallest example" of a large number, so by this definition a dust mite is not even a large number! However, I define a large number as any number exceeding 1. Thus a dust mite is a large number under this definition, but by googological standards a "small" large number).

So how big is this number really? Some figures are in order. 50,000 seconds is The equivalent of 13.8 hours. That's a pretty long time for almost any daily activity. 50,000 minutes is the equivalent of 34.7 days, just over a month! 50,000 hours is the equivalent of 5.7 years, and 50,000 days is 136 years! This means that even the longest living persons on record do not live 50,000 days. Running a facet at full force would waste 50,000 gallons of water in about 17.3 days. That's a pretty long time to be running water. If this water were turned into a sphere, it would have a diameter of 7.12 meters. This is actually quite HUGE. A person's height is only about 1.78 meters. So this sphere, resting on level ground, would tower about 4 times taller than a person!

Next we consider a slightly larger number (by a factor of 1.6) ...

(3)cheese mite = 8E4 = 8*(10^4) = 80,000

A "cheese mite" is another tiny mite, often found on cheeses. Typical size for a cheese mite is 0.40 mm for males and 0.50 mm for females. It is therefore slightly larger than a dust mite.

Likewise the number cheese mite is only slightly larger than a dust mite by a factor of 1.6. It's defined as an 8 followed by 4 zeroes. 80,000 seconds is 22.2 hours, almost an entire day. 80,000 minutes is equivalent to 55.5 days. 80,000 hours is equivalent to 9.12 years, and 80,000 days is 219 years. It would take about 27.7 days to waster 80,000 gallons of water running a facet at full force. If this water were turned into a sphere it would have a diameter of 8.33 meters. That's only 1.17 times the diameter of the sphere containing 50,000 gallons of water. How large would this sphere look next to a person? An image of a record holder for the worlds largest beach ball will give you a rough idea of just how big this is...

This beach ball is nominally 10.99 meters across (measurements are typically done when deflated. Inflated diameters are always a little smaller), but I estimate that it is closer to 8.5 meters across when inflated. Given the latter figure this beach ball is capable of holding approximately 84,800 gallons of water! The "dust-mite sphere" would take up about 58% that amount of space, and it's diameter would only be 84% of the beach ball. None the less such a sphere would still be a tad disquieting to be next to. So a dust mite is a number small enough that we can actually experience it directly, but just big enough to leave one a little easy. As for the "chees-mite-sphere" it would almost be identical to this beach ball. It's diameter would only be about 98% of the beach ball and it would take up 94% of the space.

Numbers smaller than the ten thousands become increasingly easy to wrap our brains around, but also decrease significantly in impressiveness. So we will let this represent a lower threshold to our exploration of large numbers in ExE...

Next up is a number I dub theclover mite. A clover mite is a very tiny red spider smaller than a millimeter in length but still visible to the naked eye.

The clover mite is defined as...

(4)clover mite = 2E5 = 2*(10^5) = 200,000

... or 1/5 of a million. It's 2.5 times the size of a cheese mite, and 4 times the size of a dust mite. It contains exactly 6 digits. Looks pretty tiny in decimal form. Decimal notation however is rather misleading. To gain a proper understanding of what this number means we have to consider what having 200,000 of something would actually look like. If we were to run a facet at full force it would take 69 days to waste 200,000 gallons of water! That's a lot of water. What if that water were formed into a sphere? This would be a sphere about 11.31 meters across. In comparison to the beach ball the "clover-mite-sphere" would take up 2.35 times more space and have a diameter approximately 1.33 times that of the beach ball. Here is a comparison of a eyelash mite, dust mite, cheese mite, the beach ball, and a clover mite...

These are numbers small enough that we can gain some real world understanding of it, but it's still big enough to make you feel a little intimidated. The beach ball in this example makes a person look kind of small in comparison. In fact the average volume of a person is only about the equivalent of 17.5 gallons. The beach ball in the image therefore has a volume 4840 times bigger! A clover mite is still a reasonably big number in most situations you encounter in day-to-day life. Some numbers for comparison: the average human life span measured in days is only about 27,000 or 0.14 clover mite. In your entire life time your not likely to consume somewhere in the ballpark of 13,700 gallons of water! In other words, even a clover mite gallons of water is over 14 times more water than you would need for your entire life! So as you can see, for us at least, even a clover mite is kind of a big number ... it's only a "clover mite"compare to the next giant ...

Next we consider a number that dwarfs a dust mite, and a clover mite ... the pipsqueak! We define the pipsqueak as ...

(5)pipsqueak = E7 = 10^7 = 10,000,000

...which is 50 times the size of a clover mite. To put this in some perspective we can consider another even larger spherical object taken from real life: the Unisphere. The Unisphere is a giant metal globe that was part of the 1964 world fair. It is quite huge in human terms. It has a diameter of approximately 36.5 meters, making it's diameter about 4.3 times longer than that of the beach ball. It's volume would accordingly be about 79 times greater! If we could somehow fill the entire unisphere with water it would contain approximately 6,768,000 gallons of water! Now imagine a sphere containing a pipsqueak gallons. This would take up approximately 1.477 times more space and have a diameter about 1.13 times that of the unisphere. Here is an image comparing the clover mite, Unisphere, and pipsqueak...

The diameter of the pipsqueak-sphere to the clover mite-sphere is only about 3.6 times bigger. The unisphere is itself interesting to draw comparisons with since it is a model of the much larger earth. It turns out that the earth's diameter is approximately 350,000 times greater than the Unisphere. Another crazy figure to try to wrap your brain around is that just over a million Unisphere's could be lined up end-to-end around the actual earth's circumference! Even more insane we could fit approximately 42,000,000,000,000,000 (4.2E16 or 42 quadrillion ) Unisphere's within the volume of the actual earth!

Bare in mind that numbers even in this humble regiment will soon not only dwarf the Unisphere but the actual earth ... and soon after that the known universe! The pipsqueak is big enough to actually be a little frightening. But it is a tin little "pipsqueak" in comparison to the ... little squeaker!

(6)little squeaker = 5E10 = 50,000,000,000

A little squeaker is 5000 times greater than the pipsqueak. So how vast a sphere would a little squeaker gallons of water form? It would be a sphere whose diameter was 712.3 meters. That's a diameter 19.5 times that of the Unisphere. Here is an image to bring that home...

o_0;

Now this is starting to get kind of scary! This thing would just tower menacingly above the Unisphere. "Little Squeaker"? More like super giant! But this "little squeaker" is about to look tiny next to the ...

(7)small fry = E15 = 10^15

= 1,000,000,000,000,000

This number is also known as a quadrillion in the short scale and a billiard in the long scale. A small fry is a term given to tiny young fish. It's a "small fry" only in googological terms though. It's still a very very big number! It's 20,000 times larger than the little squeaker! Gulp. So what does that mean in terms of size?!

Since we are going with fish metaphor's, let's continue our water volume analogy to give us a sense of just how gigantic the small fry really is. How large would a sphere containing a small fry gallons of water be? It would have a diameter of 19.3 kilometers. That 19,300 meters! This is a lot biggerthan a pipsqueak, and still quite a big larger than the little squeaker. The "small-fry-sphere"would have a diameter about 464 times greater than the pipsqueak, and 27 times greater than the little squeaker! To give us some idea just how huge that is we will consider how this would look hovering over manhattan along with the pipsqueak and little squeaker...

0_0;

The pipsqueak is a little smaller than a pixel at this scale! Even the little squeaker looks pretty small in comparison. The small fry is frighteningly massive! The pipsqueak is very tiny, and the clover mite and dust mite are now comparable to its namesake! But remember that little pixel representing the pipsqueak is just a little bigger than the unisphere!

This small fry-sphere would look pretty intimidating hovering over the New York sky line. In fact if you were directly beneath it the entire sky would probably go dark. Suffice it to say that a small fry is a big fryfrom any ordinary point of view. For another useful illustration we might consider what a small fry pennies might be like. A small fry pennies would be enough to cover all of manhattan 31 feet deep in pennies! What was the earth like a small fry seconds ago? This would be about 31,000,000 years ago ... long before anything we would call "human" walked on the earth but still some 34,000,000 years after the extinction of the dinosaurs. In this gigantic 31,000,000 year span of time we could fit all of recorded history 4500 times!

Numbers like this are just mind blowingly big ... and they are tame compare to what's to come ...

Finally we reach the eponymous member of this regiment, the guppy. Regiments are named after their Colonel. This is also technically a "recruit" of the regiment, but it has the distinction of being the only recruit the regiment is named after. It is usually one of the smallest and earliest members of the regiment. A guppy is a fish known for it's small size. Thus the name is chosen to reflect the fact that this is the smallest regiment in ExE. The Guppy may be thought of as a corruption and miniaturization of a googol. The guppy is defined as...

(8)guppy = E20 = 10^20

= 100,000,000,000,000,000,000

... or 1 followed by twenty zeroes. It's a number so "small" that we can write out it's decimal expansion completely! (Don't expect that to last for much longer. This is the only regiment where we can actually write down some of members in decimal). Despite the name, and it's humble status in googology, even this little "guppy" is freaking HUGE! On the entire surface of the earth there is an estimated 326,000,000,000,000,000,000 gallons of water. That's only 3.2 guppy gallons! So a guppy represents about a 1/3 of all the water on the earth measured in gallons! If we were to create a perfect sphere of this volume of water it would have a diameter of 897 kilometers. To put that in perspective the diameter of the earth is about 12,770 kilometers. This means the sphere of a guppy gallons would only be about 1/14 of the diameter of the earth. Here is an image to give you an appreciation of what that means ...

How much bigger is this "guppy sphere" in comparison to the "small fry sphere"? The guppy sphere has a volume 100,000 times greater than the small fry sphere. This means it has a diameter 46.4 times greater! Here is an image to gain some appreciation of that...

The small fry really does look like a small fry now! And the so called "guppy" looks absolutely gigantic. Just remember it's not that the small fry is small ... it's that the guppy is just THAT MUCH BIGGER! And we've only just begun...

It hasn't even been a guppy seconds since the big bang. It's only been about 432,000,000,000,000,000 seconds. A guppy seconds into the future is about 3,160,000,000,000 years from now. This is an unfathomably long time into the future. The earth and sun will have long since past away before that time! A guppy pennies would take up about 13,821 cubic miles of space. This is enough to cover all of the state of Maryland one mile deep in pennies! A guppy is no guppy by any means! It's only a guppy in comparison to the monstrosities that await us!

Next we consider another sub-googol googolism ... the minnow. The minnow is defined as...

(9)minnow = E25 = 10^25

= 10,000,000,000,000,000,000,000,000

This is yet another 100,000 times larger than the guppy. Continuing with our water analogy, a sphere containing a minnow gallons of water would have a diameter of 41,657 kilometers! That's a diameter 3.26 times greater than the earth and 46.4 times greater than the guppy-sphere! Cookie Fonster of googology wiki pointed out that the minnow-sphere would be comparable to the size of Neptune, although technically Neptune is slightly larger by about 17%. Again another visual is in order...

As promised we've reached numbers that have now dwarfed the earth itself! At this scale the guppy does indeed look like a guppy beside the earth and minnow. The small fry is now actually microscopic being only about a 1/5 of a pixel at this point! Remember how huge it felt just a short while ago in comparison to the pipsqueak and little squeaker!

The minnow is itself a relatively tiny fish in the ocean of googology ... now prepare for a real shock to the system...

(10)goby = E35 = 10^35

= 100,000,000,000,000,000,000,000,000,000,000,000

A goby is defined as 1 followed by 35 zeroes, also known as a hundred decillion. A gobyis a relatively small fish though bigger than a guppy. A goby is quite a jump in scale from the last member. We've gone up an additional 10 orders of magnitude. That means a goby is 10,000,000,000 times larger than a minnow! This is a bigger jump than any of the previous jumps.

So how big would a goby-sphere be? It would have a diameter of roughly 89,000,000 kilometers! This is so big that it dwarfs the sun! It's so big in fact that we have to compare it to a much larger object. If the goby-sphere were centered on our sun it would fit within the orbit of mercury. It would have a diameter approximately 64.4 times that of the sun, which in turn has a diameter 109 times greater than earth! It would also be only slightly smaller than the massive star Beta Orionis. Here is an image to put that all into perspective...

O_O;;;

The goby is so much larger than a minnow that I actually have to magnify the image x20 for you to be able to see it. At the original scale it would only be about 0.16 of a pixel in diameter! That's the power of just 10 order of magnitudes, and this happens ... every time we go up 10 orders of magnitude! Can things get any more insane ... remember the first law of googology ... it only gets worse ... or as the founder of googology wiki once put it ... you ain't seen nothing yet!

Next up is another corruption and miniaturization of a googol that I call a gogol. A gogol is defined as...

(11)gogol = E50 = 10^50

= 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

... or 1 followed by 50 digits. This name is based off googol but is pronounced /GO-GOL/. A gogol is much larger than a minnow, or even a goby. It's a minnow minnow's. This means that a minnow vanishes by a factor of itself when compared to a gogol! To put it bluntly, a gogol is 10,000,000,000,000,000,000,000,000 times larger than a minnow. This is such a huge jump in size, even in comparison to all our previous jumps, that it is difficult for a human to even grasp! There is almost no analogy that can help here! Imagine that a minnow is a dust mote only 0.1 mm in size, the limit of visibility. Now imagine filling Wembley Stadium solid with these dust motes ... this would still fall a little more than 6 orders of magnitude short of a gogol. Therefore you would instead need to imagine a million Wembley stadiums totally packed with such dust motes to reach about a gogol ( actual figure is closer to 2.5 million). It sounds really impressive ... but does that really make it clear? Probably not.

It might seem we have more hope comparing a gogol to a goby, but even then it's still a gap of 15 orders of magnitude, the largest jump in size so far.

Here are some insane figures for a gogol. A gogol kilograms would be about the mass of a hundred million galaxies! To go back to a previous analogy, let's see how much more monstrous a gogol-sphere is in comparison to a minnow-sphere and a goby-sphere. A gogol gallons of water contained in a sphere would be so huge that if it were centered on our sun it's radius would exceed the orbit of pluto ... 613 times!!! Remember that a guppy gallons is only a 1/3 of all the water on the earth, and a minnow gallons is only a few times the size of the earth. A minnow really sounds tiny now!

This jump in magnitude is so great that I have to magnify the image x1000 just so you can see the size of a goby and the star Beta Orionis.

Let's try to understand the gap between a minnow and a gogol, it's square. Remember the dust mite? Compare that to the minnow. Hard to do right? The ratio between those two numbers is 200,000,000,000,000,000,000. Now imagine dwarfing a minnow by the same factor! This would still be smaller than a gogol by a factor of 50,000. Mind numbing isn't it. At this point we will be lucky to get ratios small enough to really wrap our brains around. How can we get any idea how large this is? We can compare it to something roughly as large. The diameter of the gogol-sphere is about 0.95 Light years! This means it's comparable to the smallest of nebula. Here is an image of the gogol-sphere in comparison to the Cat's Eye Nebula...

@_@;

(To get a handle on just how large the Cat's Eye Nebula is you can check out my artilce Surveying the Cosmos)

Just look how tiny the goby is now! It's difficult to even understand with all of those magnifications. The really remarkable thing is that we have achieved this tremendous size by simply squaring the minnow! Powers have a lot of power! As we progress we will begin relying more and more on the idea of raising one number to some power. Just remember even squaring a number results in a horrendously larger number.

So where do we go next ? At this rate we will be dwarfing the known universe soon and running out of real world comparisons!

Next we introduce a number so large that it would swallow the milky way ...

A jumbo shrimp is 1 followed by 65 zeroes, also known as a hundred vigintillion. This is yet another 15 orders of magnitude above the gogol. In the span of these 15 orders of magnitude we go all the way from the size of nebula to the size of galaxies! A sphere containing a jumbo shrimp gallons of water would have a diameter of approximately 94,863 light years, placing it at just 95% the size of the milky way galaxy! Here is an image comparing the jumbo shrimp the milky way and the now picayune gogol ...

X_X;

We are beginning to reach a point where we really can't appreciate the size even of these little shrimps. The problem is that we can only really grasp a jump of a few orders of magnitude at a time ( I put an upperlimit of 25 orders of magnitude before there is no analogy we can actually understand to grasp the difference in magnitude). So to understand numbers like the humble jumbo shrimp we are forced to go through multiple jumps to get there, as we have done with this gradual introduction of more and more gigantic numbers. But after a while this is no longer helpful. If one number is already too huge for us to comprehend, saying another number is 15 orders of magnitude greater doesn't actually help us understand the larger number! Worse yet we will soon get to a point where the number of jumps alone becomes incomprehensible!!!

A lightweight is 1 followed by 75 zeroes. There is no officially recognized name in english for this number ( In english the names can only be extended up to 10^66-1, after while we have no name for 10^66). A lightweight is a minnow cubed! This makes it the logarithmic 3/4 point to a googol. This number is so big that there are very few things to compare it to! A sphere containing a lightweight gallons of water would have a diameter of approximately 204,376,000 light years! This is so big that we have to compare it to galaxy clusters. Here is an image of the lightweight-sphere next to the Virgo cluster...

This number is so TREMENDOUS that it is almost god-like ... but hold that thought ... we haven't even transcended the observable universe yet! Once we get past that point, we won't have anything left to compare the size to except other very large numbers. Things get really insane after that. But before we get to that ... 5 more orders of magnitude ... brings us to a ...

(14)ogol = E80 = 10^80

= 100,000,000,000,000,000,000,000,000,000,000,000,000,000

,000,000,000,000,000,000,000,000,000,000,000,000,000

An ogol is 1 followed by 80 zeroes. An ogol is so large that I can't even write it's decimal expansion on a single line. An ogol, pronounced /OH-GOL/, is another corruption of a googol. It's the fourth power of a guppy. A commonly cited figure is that the observable universe contains approximately 10^80 sub-atomic particles. Thus we can say the observable universe contains approximately an ogol particles.

How big would the sphere containing an ogol gallons of water be? It would have a diameter of approximately 9,486,000,000 light years! This makes it's volume an appreciable fraction of the observable universe (about 1/1000). Here is the ogol-sphere in comparison to the observable universe and the lightweight...

Even if we filled up the observable universe entirely with water this would only amount to approximately 9.42E82 gallons of water, about 942 ogols worth.

We are now at the precipice of the known, about to sky rocket into a dark world of unknown scales beyond! Next up is a number that will even dwarf the known universe ... as promised ...

(15)tiny twerpuloid = E85 = 10^85

= 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000

,000,000,000,000,000,000,000,000,000,000,000,000,000,000

The tiny twerpuloid is 100,000 times larger than an ogol. It's 106 times more than the number of gallons of water that could fit in the observable universe! A sphere containing a tiny twerpuloid gallons of water would have a diameter of 440,000,000,000 light years. That's roughly 4.73 times the diameter of the observable universe. Here is an image comparing the tiny-twerpuloid-sphere to the observable universe...

Despite having dwarfed everything we can currently see in the universe (the universe may be much larger than the observable portion), we are still 15 orders of magnitude from a googol...

(16)googolspeck = E90

= 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

We are now fast approaching a googol, a common benchmark in large numbers. As such a googolspeck is a number that appears to be logarithmically quite close to a googol, but appears as a tiny speck next to a googol. Hence the name.

A sphere containing a googolspeck gallons of water would have a diameter of 20,400,000,000,000 light years. That's roughly 220 times the diameter of the observable universe! Here is an image comparing the observable universe, the tiny twerpuloid, and the googolspeck ...

At this scale the observable universe is only 2 pixels in diameter! The observable universe looks like a speck beside the googolspeck. But as we will see shortly, even a googolspeck looks like a speck besides a googol. Next up is another near-googol-number ...

(17)googolcrumb = E95

= 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

A googolcrumb is 100,000 times larger than a googolspeck. Just how big would the googolcrumb-sphere be? It's no longer relevant to give it's diameter in light years, so let's start using the observable universe itself as our metric (although this will quickly become obsolete as well!). The googolcrumb-sphere with have a diameter 10,181 times the observable universe! Here is an image for the googolcrumb ...

Now you can begin to appreciate why I would call a number which literally dwarfs the observable universe a tiny twerpuloid. It's actually microscopic next to the googolcrumb. A googolcrumb is itself just a "crumb" off of a googol. Now for a number very close to a googol ...

That's 1 followed by 99 zeroes. It's 10,000 times larger than a googolcrumb, but it's only 1/10th of a googol! At such large scales, a difference of 10 is extremely close. In fact, the ratio of the diameters of a googolchunk-sphere vs. a googol-sphere would only be about 2.15. Here is an image comparing a googolchunk to a googol, as well as to a bunch of smaller googolism's we've already reviewed...

In this scale we can properly see how a googolchunk represents a sizable "chunk" of a googol, how a googolcrumb is just a "crumb" of a googol, how a googolspeck is literally just a very tiny "speck" next to a googol, and how a tiny twerpuloid, a number which dwarfs the known universe, is just a teeny tiny twerp in the mindboggling world of googology!

At just ten googolchunk's we reach a googol. We can consider this an important benchmark between numbers which are large in the conventional sense, and numbers which are large in the googological sense. Although we can go further still with this sphere comparison game, at some point all sense is lost because we have nothing to compare the sphere's to except each other. Furthermore, if we want the jumps to be comprehensible, we can only jump a few orders of magnitude at a time, but then we will never succeed at getting to any of the larger googolism's in this regiment, let alone anything further than that!

None the less it would be nice to have some operators that could give us multiples of a googol rather than fractions of a googol. I suggest the use of -bunch, -crowd, and -swarm, to mean x10 , x10^5 , and x10^10 respectively. This is analogous to -chunk, -crumb, and -speck which meant 1/10 , 1/10^5, and 1/10^10 respectively. With this is in mind we form...

(19)googolbunch = 10*E100 = E101 = 10^101

(20)googolcrowd = 100,000*E100 = E105 = 10^105

(21)googolswarm = 10,000,000,000*E100 = E110 = 10^110

A googolswarm is as big compare to a googol as a googol is compare to a googolspeck! It's amazing to contemplate ... and yet it only amounts to 10^110 which seems like it's barely an improvement at this point. That's because we've already gone through so many orders of magnitude that another "10" doesn't seem as much of a big deal. We are going to need much more powerful operators to make progress in googology! But before we get to that dizzying prospect, I'd us to consider what we've done so far to figure out what other googolism's we can form and where to go from there.

We have created an ad-hoc series of names for different names, none really having much to do with another, except in the case of our modifiers on a googol. If you think about it we can actually use these as general operators on any number. Just let...

(n)-speck = n/10,000,000,000

(n)-crumb = n/100,000

(n)-chunk = n/10

(n)-bunch = 10*n

(n)-crowd = 100,000*n

(n)-swarm = 10,000,000,000*n

How many "base" googolism's do we have at this point? We have: eyelash mite, dust mite, cheese mite, clover mite, pipsqueak, little squeaker, small fry, guppy, minnow, goby, gogol, jumbo shrimp, lightweight, ogol, tiny twerpuloid, ... and googol. That's it! That's a total of 16 base googolism's. We may consider this just the first dimension of how numbers are named in the guppy regiment. The second dimension is to apply a size-modifier. There are 6 modifiers and there is also the option of having no modifier. So there are 7 possible states in the second dimension. The result is that we can theoretically have a total of 16x7 = 112 googolism's! Not bad. There is a certain degree of redundancy, as multiple names sometimes map to the same number. This is a consequence of the fact that the numbers are relatively close together and the choice of base googolism's and size-modifiers. None the less we can think of all of these as distinct constructions. That is, they are different ways at arriving at the same numbers, and thus distinct googolism's. Another weird thing is that we can get some ridiculously small numbers this way ... really stretching the idea of a "googolism".

Because applying the modifiers to the base googolism's is kind of a hit or miss aesthetically, we can make slight changes where needed to make things roll off the tongue better. We can begin with a truly weird idea of having just a "speck" of an eyelash mite. Here's what we get applying of modifiers to our base googolisms...

(22)eyelash mite-speck = 20,000/10,000,000,000 = 0.000002

o_0; Now that ... is a tiny number! In fact calling this a "googolism" is a stretch. For special names for really small numbers I suggest the term "micronym".

(23)dust mite-speck = 50,000/10,000,000,000 = 5E(-6) = 0.000005

(24)cheese mite-speck = 80,000/10,000,000,000 = 8E(-6) = 0.000008

(25)clover mite-speck = 200,000/10,000,000,000 = 2E(-5) = 0.00002

At 10 times the size of an eyelash mite-speck a clover mite-speck is still an exceptionally small googolism which is 50,000 times smaller than 1!

We can even go out of our way to create micronyms, but the easiest way to do this is just to take the reciprocal of a large number. Oddly enough Conway suggested a way to form micronyms using (n)-minex = 10^(-n). I suggest the alternative (n)-minutia = 1/n. Thus we can form a some really small micronyms as follows...

(26)guppy-minutia = 1/E20 = E-20 = 10^-20

(27)minnow-minutia = 1/E25 = E-25 = 10^-25

(28)goby-minutia = 1/E35 = E-35 = 10^-35

(29)gogol-minutia = 1/E50 = E-50 = 10^-50

(30)ogol-minutia = 1/E80 = E-80 = 10^-80

(31)googol-minutia = 1/E100 = E-100 = 10^-100

(32)googol-minutia-speck = E(-100)/E10 = E-110 = 10^-110

We can get even smaller than this but this will suffice for now...

Next let's consider the crumb version of the "mites" ...

(33)eyelash mite-crumb = 20,000/100,000 = 2E(-1) = 0.2

This is a giant compare to the previous numbers!

(34)dust mite-crumb = 50,000/100,000 = 5E(-1) = 0.5

... quite an odd name for a half ...

(35)cheese mite-crumb = 80,000/100,000 = 8E(-1) = 0.8

(36)clover mite-crumb = 200,000/100,000 = 2E0 = 2

Finally we reach a number larger than 1 (a "large number" by my usual definition). Moving on to the chunk modifier we start getting some decent sized numbers...

(37)eyelash mite-chunk = 20,000/10 = 2E3 = 2000

Counting to 2000 is a rather laborious task that can easily take up to an hour, so that's already a sizable number...

(38)dust mite-chunk = 50,000/10 = 5E3 = 5000

(39)cheese mite-chunk = 80,000/10 = 8E3 = 8000

(40)clover mite-chunk = 200,000/10 = 2E4 = 20,000

And now we return once again to the eyelash mite (20,000) the very number we began with! Well time to start climbing slowly back up to the googol. Let's start applying the large modifiers...

(41)eyelash mite-bunch = 20,000*10 = 2E5 = 200,000

Once again we have the clover mite (200,000) ...

(42)dust mite-bunch = 50,000*10 = 5E5 = 500,000

(43)cheese mite-bunch = 80,000*10 = 8E5 = 800,000

(44)clover mite-bunch = 200,000*10 = 2E6 = 2,000,000

Nowwe jump another 4 orders of magnitude with the -crowd modifier...

(45)eyelash mite-crowd = 20,000*100,000 = 2E9 = 2,000,000,000

(46)dust mite-crowd = 50,000*100,000 = 5E9 = 5,000,000,000

(47)cheese mite-crowd = 80,000*100,000 = 8E9 = 8,000,000,000

(48)clover mite-crowd = 200,000*100,000 = 2E10 = 20,000,000,000

That's only 2.5 times smaller than a little squeaker, so pretty big already. Now we can have miteswarms ...

So a clover mite-swarm is as large as 2 small fry's. So as you can see in ordinary terms these size-modifiers are quite powerful and cover 20 orders of magnitude. A huge gap by most accounts. These modifiers will rapidly become obsolete though as we progress, even just through the guppy regiment, which we've only just begun.

We may consider even smaller versions of the guppy, minnow, goby, gogol, ogol and googol by using another type of modifier. A guppy is defined as 1 followed by twenty zeroes, in decimal, but what if we had 1 followed by 20 zeroes in binary? I call this number a guppybit, and it's among the smallest of numbers in ExE...

(53)guppybit = 2^20

= 1,048,576

This is a number so small that it's actually feasible for a human to count to it! A guppybit is also the number of bytes in a megabyte. If you were to run a facet at full force for a whole year ... you would have wasted about a guppybit gallons. o_0; Impressive for such a tiny number. We can also consider a guppybyte, defined as 1 followed by 20 zeroes in octal...

(54)guppybyte = 8^20

= 1,152,921,504,606,846,976

This number has exactly 19 digits. It's exactly the cube of a guppybit, meaning it's equal to a guppybit guppybit guppybits. The guppybit would therefore be pretty minuscule beside the guppybyte.

We can also use our -bit and -byte operators on the minnow, goby,gogol, and ogol to form many more googolism's...

(55)minnowbit = 2^25 = 33,554,432

(56)minnowbyte = 8^25 = 37,778,931,862,957,161,709,568

(57)gobybit = 2^35 = 34,359,738,368

(58)gobybyte = 8^35 = 40,564,819,207,303,340,847,894,502,572,032

(59)gogolbit = 2^50

= 1,125,899,906,842,624

The gogolbit contains exactly 16 digits. It's a ridiculously huge number. You'd have to run your facet at full force for over a billion years to waste this many gallons of water. You'd have to start running your facet well before the cambrian explosion to have wasted that many gallons by the present time! That being said ... even the guppy is bigger than this number by 5 orders of magnitude. For a much larger number we jump to ...

(60)gogolbyte = 8^50

= 1,427,247,692,705,959,881,058,285,969,449,495,136,382,746,624

This number is the cube of a gogolbit.

Next we apply the -bit/-byte operators to an ogol ...

(61)ogolbit = 2^80 = 1,208,925,819,614,629,174,706,176

(62)ogolbyte = 8^80

We can also apply these operators to a googol to form new googolism's...

(63)googolbit = 2^100

= 1,267,650,600,228,229,401,496,703,205,376

This number contains exactly 31 digits. This number is sometimes referred to as little googol.

This number has 91 digits. Even though it seems to only be a little smaller than a googol, a googol is actually about 4.9 billion times it's size! This would make it appear very small in comparison in a googol. This number is also approximately 2.03 googolspeck's.

What about all the other googolism's we introduced earlier. Can we also form binary and octal versions of these? One problem is somewhat aesthetic. Some of the names don't sound good ending in -bit or -byte. It seems particularly odd to append these to the googolism's with more than one word. The other problem is mathematical. How do we interpret numbers not beginning with 1 in binary? To solve these problems I'll introduce the binary- and octal- prefixes to be used if the -bit and -byte operators sound out of place. In order to provide a universal way to interpret any of these googolism's with the binary- and octal- operator, we will let mEn = m*(10^n) be reinterpreted as m*(2^n) under the binary- operator and m*(8^n) under the octal- operator. With that we have many more googolism's we can form. Some of these are ridiculously small numbers, so small that they are only "large numbers" in the technical sense, but lack that "WOW" factor. Also there are in some cases more than one googolism possible for a particular number. None the less these are still valid constructions...

(65)binary-eyelash mite = 2*2^4 = 32

(66)octal-eyelash mite = 2*8^4 = 8192

(67)binary-dust mite = 5*2^4 = 80

(68)octal-dust mite = 5*8^4 = 20,480

(69)binary-cheese mite = 8*2^4 = 128

(70)octal-cheese mite = 8*8^4 = 32,768

(71)binary-clover mite = 2*2^5 = 64

(72)octal-clover mite = 2*8^5 = 65,536

(73)binary-pipsqueak = 2^7 = 128

( also binary-cheese mite. See #35 )

(74)octal-pipsqueak = 8^7 = 2,097,152

In the case of the little squeaker, we may drop the adjective "little" for a better sounding name...

(75)binary-squeaker = 5*2^10 = 5120

(76)octal-squeaker = 5*8^10 = 5,368,709,120

(77)binary-small fry = 2^15 = 32,768

( also octal-cheese mite. See #36 )

(78)octal-small fry = 8^15 = 35,184,372,088,832

Next we would logically apply the binary and octal operators to jumbo shrimp, but this does not lead to a very palatable name. Instead I have opted to use "prawn" as a synonym for "jumbo shrimp", thus we obtain the more palatable names...

One odd consequence of the chosen definition for the base change is that a ternary-cheese mite ends up being bigger than a ternary-clover mite. This also is the case with a binary-cheese mite (128) vs. the binary-clover mite (64). This is just a quirk of the system.

We can continue our journey by introducing a series of modifiers on the guppy, gogol, and googol. Each of these modifiers changes the base value the definition of a guppy/gogol/googol to some multiple of that value. The currently supported modifiers are -ding,-chime, -bell, -toll, -gong, -bong, -throng, and -gandingan. The definitions we will use are -ding multiplies the base value by 5, -chime by 10, -bell by 50, -toll by 100, -gong by 1000, -bong by 10^6, -throng by 10^9, and -gandingan by 10^12.

We can begin by introducing the -ding modifier. We can combine it with our previous numbers to obtain more googolisms. We can begin with the guppy. This allows us to form guppyding. Since a guppy = E20, a guppyding = E(20*5) = E100. So a guppyding is the same as a googol.

This number is still small enough that I can actually write out it's decimal expansion. This number is quite large though. It's more than the number of elementary particles in the known universe (10^80), more than the number of planck volumes in the observable universe (10^183). To get numbers this big ( or bigger ) in astronomy we need to either consider exotic theories of the universe as a whole, or consider certain hypothetical time scales for the lifetimes of certain celestial objects. We'll be getting to those shortly.

We can also consider creating binary and octal versions of the numbers guppyding, gogolding, and googolding. However the -bit and -byte operators do not sound very good here, so I suggest the alternative of appending the words binary- and octal- to the numbers...

A googolchime is exactly the square of a googolding. In other words a googolchime is equal to a googolding googoldings. A googolding would be a vanishingly small dot in comparison! This is also the tenth power of a googol. Despite the fact that we can write out a googolchime in decimal, the numbers are already far too horrendously large for us to really have a proper appreciation for. Given that, surely no number in science can possibly compare to this behemoth, right? Actually there are numbers in astronomy even larger than this. It is hypothesized that in about 10^1500 years into the future we will enter the Age of the Iron Stars, assuming protons do not decay. At this point the universe will be mostly composed on Iron-56 atoms, mostly contained within Iron Stars, unimaginably far apart from each other. It is difficult to imagine the sheer vast cold emptiness of such a future time. But we have only begun to contemplate big numbers ... next up is the massive googolbell ...

A googoltoll is the square of a googolbell. In other words a googoltoll is a googolbell googolbells. It's also the tenth power of a googolchime! That's a googolchime googolchime googolchime googolchime googolchime googolchime googolchime googolchime googolchime googolchime's!

Next up is a googolgong ...

(214)googolgong = E100,000 = 10^100,000

= 10,000,000,000,000,000 ... ... ... ... ,000,000,000,000,000

w/100,000 0s

At this point while it is still technically feasible to write out the decimal expansion in full it is becoming increasingly impractical, and soon it will be not even possible! A googolgong is the tenth power of agoogoltoll. This number defies comprehension already but ... we are still just getting warmed up with the guppy regiment ... next up is the googolbong ...

(215)googolbong = E100,000,000 = 10^100,000,000

That's 1 followed by a hundred million zeroes. This is also the thousandth power of a googolgong. At this point we have a number so big that even if you converted every character in this entire webbook into zeroes you still would not have nearly enough to write out the full decimal expansion of this number!

Going further still we have ...

(216)googolthrong = E100,000,000,000 = 10^100,000,000,000

... or 1 followed by a hundred billion zeroes. This is also the thousandth power of a googolbong. At this point we quickly eclipse the previous number to the size of an infinitesimal point every single time we go to the next googolism! We can follow with...

(217)googolgandingan = E100,000,000,000,000

A googolgandingan is 1 followed by a hundred trillion zeroes. It can also be written as 10^10^14. The name comes from the instrument of a gandingan which is composed of four gongs in series. This also suggests the name googolquadrigong and the further continuation ...

At this point we have crossed a critical point with our numbers. Given that there is only 10^80 particles in the known universe, we can conclude that there is no way to write out the full decimal expansions of integers larger than 10^10^80.

We have also crossed another critical boundary. It has been computed that Iron Stars will have life-times on the order of 10^10^76 years before collapsing into black holes. What this means is that the universe may continue to contain matter for the next 10^10^76 years at most (assuming proton decay doesn't eliminate all the matter much sooner in a mere 10^40 years). So at this point we have crossed over from mainstream astronomy into the deep end of hypothetical astronomy. We aren't quite beyond the exosphere of science yet ... but we are definitely getting to it's fringes ...

(236)googolquadragintigong = EE122 = 10^10^122

We have passed the googolplex for the first time! There are only a few more numbers less than a googolplex in the guppy regiment left.

(237)googolquinquagintigong = EE152 = 10^10^152

(238)googolsexagintigong = EE182 = 10^10^182

(239)googolseptuagintigong = EE212 = 10^10^212

(240)googoloctogintigong = EE242 = 10^10^242

(241)googolnonigintigong = EE272 = 10^10^272

(242)googolcentigong = EE302 = 10^10^302

o_0; There is an awesome number! We can go a bit further with our latin numbers to obtain...

(243)googolmilligong = EE3002 = 10^10^3002

and finally...

(244)googolmilli-milligong = EE3,000,002 = 10^10^3,000,002

At this point even the number of digits (1+10^3,000,002) is incomprehensible!!! Yet ... we are still just getting warmed up with the guppy regiment, let alone the higher regiments!

Further googolism's for the regiment can be formed by appending the suffixes -plex, -duplex, -triplex, etc. to our already modified terms on the googol.

We begin with the Guppy Series. Firstly we define a series of names with guppy combined with the gong suffixes...

(245)guppybell = E1000 = 10^1000

(also a googolchime )

(246)guppytoll = E2000 = 10^2000

(247)guppygong = E20,000 = 10^20,000

(248)guppybong = E20,000,000 = 10^20,000,000

(249)guppythrong = E20,000,000,000 = 10^20,000,000,000

(250)guppygandingan = E20,000,000,000,000 = 10^20,000,000,000,000

Let's also apply these suffixes to the gogol and ogol ...

(251)gogolbell = E2500 = 10^2500

(252)gogoltoll = E5000 = 10^5000

(253)gogolgong = E50,000 = 10^50,000

(254)gogolbong = E50,000,000 = 10^50,000,000

(255)gogolthrong = E50,000,000,000 = 10^50,000,000,000

(256)gogolgandingan = E50,000,000,000,000 = 10^50,000,000,000,000

...

(257)ogolding = E400 = 10^400

(258)ogolchime = E800 = 10^800

(259)ogolbell = E4000 = 10^4000

(260)ogoltoll = E8000 = 10^8000

(261)ogolgong = E80,000 = 10^80,000

(262)ogolbong = E80,000,000 = 10^80,000,000

(263)ogolthrong = E80,000,000,000 = 10^80,000,000,000

(264)ogolgandingan = E80,000,000,000,000 = 10^80,000,000,000,000

We can retroactively define (n)-plex as 10^n, based on treating the -plex ingoogolplex as a modifier taking "googol" as an argument. -duplex may thought of as a shortened version of-plex-plex, thus (n)-duplex should be 10^10^n. Likewise (n)-triplexis equivalent to (n)-plex-plex-plex thus 10^10^10^n. We can go further by applying latin numbers, ie. -quadriplex , -quintiplex, etc. This suggests the term guppyplex. With that in mind we can form the following Guppy Series:

guppy = 10^20 = E20

(265) guppyplex = 10^10^20 = EE20 = E20#2

(also called googolsextigong. See Member No.173 )

If the guppy was small relative to the googol, the guppyplex is inconceivably tiny relative to the googolplex. You'd have to raise a guppyplex to the 10^80 power to get to a googolplex!

(266)guppyduplex= 10^10^10^20 = EEE20 = E20#3

(267)guppytriplex = 10^10^10^10^20 = EEEE20 = E20#4

(268)guppyquadriplex = 10^10^10^10^10^20 = EEEEE20 = E20#5

(269)guppyquintiplex = 10^10^10^10^10^10^20 = EEEEEE20 = E20#6

(270)guppysextiplex = E20#7

(271)guppyseptiplex = E20#8

(272)guppyoctiplex = E20#9

(273)guppynoniplex = E20#10

(274)guppydeciplex = E20#11

...

(275)guppyvigintiplex = E20#21

(276)guppytrigintiplex = E20#31

(277)guppyquadragintiplex = E20#41

(278)guppyquinquagintiplex = E20#51

(279)guppysexagintiplex = E20#61

(280)guppyseptuagintiplex = E20#71

(281)guppyoctogintiplex = E20#81

(282)guppynonagintiplex = E20#91

(283)guppycentiplex = E20#101

...

(284)guppymilliplex = E20#1001

(285)guppymilli-milliplex = E20#1,000,001

o_0;

That's the end of the Guppy Series. But we still have lots of more series to go through. Next up is the Googolbit Series. We might append -plex at the end of this to form googolbitplex, but in the case where a modifier is already being applied to a googol I prefer to flip the order to googolplexibit. This suggest the following series...

googolbit = 2^100

(286) googolplexibit = 2^2^100 = 2^100#2

A googolplexibit is approximately 10^10^30, and falls between a guppyplex and a googolplex.

(287)googolduplexibit = 2^2^2^100 = 2^100#3

(288)googoltriplexibit = 2^2^2^2^100 = 2^100#4

(289)googolquadriplexibit = 2^2^2^2^2^100 = 2^100#5

(290)googolquintiplexibit = 2^2^2^2^2^2^100 = 2^100#6

(291)googolsextiplexibit = 2^100#7

(292)googolseptiplexibit = 2^100#8

(293)googoloctiplexibit = 2^100#9

(294)googolnoniplexibit = 2^100#10

(295)googoldeciplexibit = 2^100#11

...

(296)googolvigintiplexibit = 2^100#21

(297)googoltrigintiplexibit = 2^100#31

(298)googolquadragintiplexibit = 2^100#41

(299)googolquinquagintiplexibit = 2^100#51

(300)googolsexagintiplexibit = 2^100#61

(301)googolseptuagintiplexibit = 2^100#71

(302)googoloctogintiplexibit = 2^100#81

(303)googolnonagintiplexibit = 2^100#91

(304)googolcentiplexibit = 2^100#101

...

(305)googolmilliplexibit = 2^100#1001

(306)googolmilli-milliplexibit = 2^100#1,000,001

Next up the Gogol Series ...

gogol = 10^50 = E50

(307)gogolplex = 10^10^50 = EE50 = E50#2

The gogolplex is not half of a googolplex. Instead you'd have to raise a gogolplex to a gogol to get a googolplex!

(308)gogolduplex = 10^10^10^50 = EEE50 = E50#3

(309)gogoltriplex = 10^10^10^10^50 = EEEE50 = E50#4

(310)gogolquadriplex = 10^10^10^10^10^50 = EEEEE50 = E50#5

(311)gogolquintiplex = 10^10^10^10^10^10^50 = EEEEEE50 = E50#6

(312)gogolsextiplex = E50#7

(313)gogolseptiplex = E50#8

(314)gogoloctiplex = E50#9

(315)gogolnoniplex = E50#10

(316)gogoldeciplex = E50#11

...

(317)gogolvigintiplex = E50#21

(318)gogoltrigintiplex = E50#31

(319)gogolquadragintiplex = E50#41

(320)gogolquinquagintiplex = E50#51

(321)gogolsexagintiplex = E50#61

(322)gogolseptuagintiplex = E50#71

(323)gogoloctogintiplex = E50#81

(324)gogolnonagintiplex = E50#91

(325)gogolcentiplex = E50#101

...

(326)gogolmilliplex = E50#1001

(327)gogolmilli-milliplex = E50#1,000,001

Next up is the Googolbyte Series ...

googolbyte = 8^100

(328)googolplexibyte = 8^8^100 = 8^100#2

(329)googolduplexibyte = 8^8^8^100 = 8^100#3

(330)googoltriplexibyte = 8^8^8^8^100 = 8^100#4

(331)googolquadriplexibyte = 8^8^8^8^8^100 = 8^100#5

(332)googolquintiplexibyte = 8^8^8^8^8^8^100 = 8^100#6

(333)googolsextiplexibyte = 8^100#7

(334)googolseptiplexibyte = 8^100#8

(335)googoloctiplexibyte = 8^100#9

(336)googolnoniplexibyte = 8^100#10

(337)googoldeciplexibyte = 8^100#11

...

(338)googolvigintiplexibyte = 8^100#21

(339)googoltrigintiplexibyte = 8^100#31

(340)googolquadragintiplexibyte = 8^100#41

(341)googolquinquagintiplexibyte = 8^100#51

(342)googolsexagintiplexibyte = 8^100#61

(343)googolseptuagintiplexibyte = 8^100#71

(344)googoloctogintiplexibyte = 8^100#81

(345)googolnonagintiplexibyte = 8^100#91

(346)googolcentiplexibyte = 8^100#101

...

(347)googolmilliplexibyte = 8^100#1001

(348)googolmilli-milliplexibyte = 8^100#1,000,001

however I find this doesn't sound as good as reversing the order of the suffixes, thus googolplexichime, a modification of the googolplex. From this we may form the following continuation:

We begin with the Googolchime Series. We can retroactively define (n)-plex as 10^n, based on treating the -plex in googolplex as a modifier taking "googol" as an argument. -duplex may thought of as a shortened version of -plex-plex, thus (n)-duplex should be 10^10^n. Likewise (n)-triplex is equivalent to (n)-plex-plex-plex thus 10^10^10^n. We can go further by applying latin numbers, ie.

-quadriplex , -quintiplex, etc. This suggests the term googolchimeplex, however I find this doesn't sound as good as reversing the order of the suffixes, thus googolplexichime, a modification of the googolplex. From this we may form the following continuation:

Is that it?! Not quite. I also have a continuation of thecentillion. It seemed natural to me to continue from the centillion with 1 followed by a centillion zeroes, and then 1 followed by THAT, then THAT, and so on. However I could not devise any good names for these numbers, other than the erroneous centillionillion. With the introduction of such suffixes as -plex, -duplex, -triplex, etc. the continuation seems obvious. However rather than use the predictable "centillionplex", which doesn't sound that great, I propose a new "base". Let "Eceton" be another name forcentillion. Then we can define the following numbers:

(425) ecetonplex = E303#2 = 10^10^303

(426) ecetonduplex = E303#3 = 10^10^10^303

(427) ecetontriplex = E303#4 = 10^10^10^10^303

(428) ecetonquadriplex = E303#5 = 10^10^10^10^10^303

(429) ecetonquintiplex = E303#6 = 10^10^10^10^10^10^303

(430)ecetonsextiplex = E303#7 = 10^10^10^10^10^10^10^303

(431)ecetonseptiplex = E303#8 = 10^10^10^10^10^10^10^10^303

(432)ecetonoctiplex = E303#9 = 10^10^10^10^10^10^10^10^10^303

(433)ecetonnoniplex = E303#10 = 10^10^10^10^10^10^10^10^10^10^303

(434)ecetondeciplex = E303#11 = 10^10^10^10^10^10^10^10^10^10^10^303

...

(435)eceton-vigintiplex = E303#21

(436)eceton-trigintiplex = E303#31

(437)eceton-quadragintiplex = E303#41

(438)eceton-quinquagintiplex = E303#51

(439)eceton-sexagintiplex = E303#61

(440)eceton-septuagintiplex = E303#71

(441)eceton-octogintiplex = E303#81

(442)eceton-nonagintiplex = E303#91

(443)eceton-centiplex = E303#101

...

(444)eceton-milliplex = E303#1001

(445)eceton-millimilliplex = E303#1,000,001

For fun here are some additional numbers we can name using -eceton- along with some of the other modifiers...

Another thing I'd like to introduce is a nice way to name the so called millionplex along with a bunch of other googolism's patterned on the same approach. Since millionplex never sounded very good to me I suggest reordering the roots as milliplexion. From this we can get...

In addition I'd like to coin a name for a number my brother came up with while struggling to show that creating "very large numbers" is always easy...

(469)fzmilliplexion = (10^1,000,000)^(10^1,000,000)

= 10^(1,000,000*10^1,000,000) = 10^10^1,000,006 = E1,000,006#2

This can alternatively be defined as (10^10^1,000,000)^1,000,000. In other words it is the millionth power of a milliduplexion. With numbers this big however this isn't that impressive an improvement. While it is true that this number is easy to define ... using modern decimal and exponential notation ... this isn't what I mean when I speak of numbers so large they are "hard" to define. We need to create rather sophisticated recursions to reach that level. We have really only just begun ...

In addition to all this I also have some
names for power towers of Tens. The number of tens can be written as a
greek number followed by the suffix "-logue". Thus I define the
following numbers:

The hectalogue is a
number so huge that you have to take the common logorithm of it a
hundred times to reduce it to a one ! That's so counter-intuitive it
sounds impossible, but it's not! The dekalogue is also known as the "decker" in Bowers system, and the hectalogue is known as the "giggol".

We can go a little further with the greek numbers, so let's also introduce:

(498) chilialogue = E1#1000

= 10^10^10^10^ ... ... ... ... ^10^10^10^10

(w/1000 Tens)

(499)myrialogue = E1#10,000

= 10^10^10^10^ ... ... ... ... ^10^10^10^10

(w/10,000 Tens)

(500)chilia-chilialogue = E1#1,000,000

(501)chilia-myrialogue = E1#10,000,000

(502)myria-myrialogue = E1#100,000,000

We can go a little further ... but there aren't many classical greek words for larger numbers. We could coin...

(503)octadalogue = E1#100,000,000

As an alternative to a myria-myrialogue using Archimedes "octad". Going a little further with this pattern we could use...

(504)sedeniadalogue = E1#10,000,000,000,000,000 = E1#(10^16)

That's as far as we can go with the greek. At this point we are really pushing the limits of the guppy regiment, so let's stop here.

The numbers in the "Guppy Regiment" are already large enough to exceed anything we'd need in the sciences. There is very little practical use for numbers as large as a hectalogue. Yet this is only just the beginning of what we can define mathematically! In the next regiment we will quickly make the sedeniadialogue look like a guppy in comparison ...

Grangol

Regiment

Category 2

Members: 188

(505 - 692)

Now for something a little
more interesting. Let's begin by extending the "googol series" to
insane heights. Let a googol = E100, be "step 1". Let a googolplex =
EE100 be "step 2". Let a googolduplex = EEE100 be "step 3". Continue
this way until you reach the 100th step. This is some new kind of
number. I will call it a "grangol", which is short for "grand googol".
Now we can say:

(Note: The grangol is comparable to the giggol, though it's "slightly" larger)

That's a pretty cool
number. We can also have a ...

(506)grangolbit = 2^100#100

and a ...

(507)grangolbyte = 8^100#100

But ... you might be thinking ... these numbers aren't much larger than a hectalogue (E1#100), and are certainly smaller than even a chilialogue (E1#1000). This is true. There is some overlap here between the guppy regiment and the grangol regiment. So just to prove a point let's push the whole -logue idea to the limit. Then I'll show that we can still beat this with tricks exclusive to the grangol regiment. First to go further we loosen the requirement that the argument for (n)-logue need be in greek. Thus we can use our googolism's to bootstrap us to even larger values. Here are some examples...

But to go much further than this we can just loosen the requirement that the argument be in greek. With this in mind I will coin the largest numbers of this regiment...

... at this point the constant nesting of the -logue operator becomes difficult to read and say. What would be even better? If we could get the same recursion with our new grangol number. We can have a grangol 10's with a
determinant of 100, or the grangolth member of the googol series. We
can't use "plex" here. If we use the definition we established in the
"googol series" article (3-1-4). Technically we would have to say:

(544) grangolplex = E(E100#100) = E100#101

Therefore
I suggest a new prefix, called "dex". The "dex" simply takes the
number, and substitutes it back into the replicator. Basically the "dex"
function generates a power tower with a height equal to it's input! We
can then define the following numbers:

We can also use the "dex" and "plex" suffixes in non-standard ways to create even more numbers. Whenever converting a name involving mixed types of suffixes, apply the suffixes from left to right. Here are some examples:

We can also apply our suffixes to other numbers besides a grangol. Here's what happens when we apply them to Jonathan Bowers' giggol:

(644) giggolchime = E1#1000 = 10^10^...^10^10 w/1000 10s

(645)giggoltoll = E1#10,000 = 10^10^...^10^10 w/10,000 10s

(646)giggolgong = E1#100,000 = 10^10^...^10^10 w/100,000 10s

(647)giggolbong = E1#100,000,000

(648)giggolthrong = E1#100,000,000,000

For extending the centillion into this range we can use these names:

(649) ecetondex = E303#1#2 = E303#(E303) = E303#centillion =

10^10^10^ ... ... ^10^10^303 (w/centillion tens!)

(650) ecetondudex = E303#1#3 = E303#ecetondex

(651) ecetontridex = E303#1#4 = E303#ecetondudex

(652) ecetonquadridex = E303#1#5 = E303#ecetontridex

(653) ecetonquintidex = E303#1#6 = E303#ecetonquadridex

(654) ecetonsextidex = E303#1#7

(655)ecetonseptidex = E303#1#8

(656)ecetonoctidex = E303#1#9

(657)ecetonnonidex = E303#1#10

(658)ecetondecidex = E303#1#11

We can also come up with some names for common tetra-towers. I will use the suffix "-taxis" , meaning "class", to indicate the tetrational-logarithm , or taxirithm. Thus I define the following numbers:

The
innermost E100#100 is a grangol, and is the first step. E100#(E100#100)
is a grangoldex and is the second step. E100#(E100#(E100#100)) is a
grangoldudex and is the third step. A greagol is the 100th step of the grangol series!

Here is a visual representation of a greagol:

Next we come up with a new suffix, the "-threx", to have as many levels of power towers as the previous number. Thus:

A hecta-petaxis is equivalent to 10^^^^100, which is known as a "geegol" in Bowers system. Furthermore ...

(767) chilia-petaxis = E1#1#1#1000

(768) myria-petaxis = E1#1#1#10,000

At this point it's impossible for us to fully appreciate the gaps between these enormous numbers. The difference between a grangol and a grangoldex is already staggeringly counter intuitive. It's almost impossible to appreciate the huge gulf that must exist between a greagol and a greagolthrex.

Gigangol

Regiment

Category 4

Members: 59

(769 - 827)

Next comes the "gigangol" (short for gigantic googol). By definition:

(769) gigangol = E100#100#100#100

Gigangol is comparable to and slightly larger than a geegol.

At this point it is
difficult to describe these numbers using the conventional illustrations
of power towers. A gigangol is the 100th member of the series,
beginning with greagol, greagolthrex, greagolduthrex, etc. In other words its the 100th member of the greagol series.

To help visualize this number we can use the following special notation. Let:

rb#d = b^b^b^ ... ^b^b^d w/r b's

Using this notation we can say that:

grangol = 10010#100

We can now express the greagol more compactly than before as:

In this way we can now express gigangol in an expanded form:

Even in this expanded form we aren't really getting the full picture. It would have to be expanded further just to see what's going on with the power towers, and forget about imagining how many digits this number has!!!

And yet it is virtually no trouble at all to go much much further. Just define a new prefix, the "-tetrex" and define:

The hecta-octaxis is equivalent to 10^^^^^^^100, also known as the "gagol" in Bowers' System.

Finally we have...

(927)chilia-octaxis = E1#1#1#1#1#1#1000

(928)myria-octaxis = E1#1#1#1#1#1#10,000

Gaspgol

Regiment

Category 7

Members: 46

(929 - 974)

Due to the popularity of my extension of the classic googol-series, some have tried to extend it beyond the Gulgol group. In response to this I created the 7th group of the main series: the Gaspgol Regiment (the gaspgol is short for the *gasp* googol), and the 8th, the Ginorgol Regiment.

Predictably the gaspgol is defined as:

(929) gaspgol = E100#100#100#100#100#100#100

(Note: the gaspgol is comparable to and slightly greater than the "gagol" of Bowers' System)